Adaptive control of bifurcation and chaos in a time-delayed system

• Published in: Chinese physics B Vol. 22; no. 3; pp. 245 - 255
• Main Author: 李宁 袁惠群 孙海义 张庆灵
• Format: Journal Article
• Language: English
• Published: 01.03.2013
• Subjects: Adaptive control; Adaptive control systems; Bifurcations; Chaos theory; Control systems; Hybrid control; Mathematical models; Perturbation methods; Stability; 分岔; 参数扰动; 控制参数; 时间延迟系统; 混合控制方法; 混沌; 渐近稳定性; 自适应控制
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/22/3/030508

In this paper,the stabilization of a continuous time-delayed system is considered.To control the bifurcation and chaos in a time-delayed system,a parameter perturbation control and a hybrid control are proposed.Then,to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes,the adaptive control idea is introduced,i.e.,the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws,respectively.The adaptation algorithms are constructed based on the Lyapunov-Krasovskii stability theorem.The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods.They have the advantages of increased stability,adaptability to the changes of the system parameters,control cost saving,and simplicity.Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods.A comparison of the two adaptive control methods is also made in an experimental study.